Recaps

After receiving their project payments, Xiao Yi said goodbye to Terence Tao and James Maynard and traveled with Zhang Yitang to Santa Barbara. They reviewed the remaining obstacles to the Landau-Siegel Zero Conjecture and began working on them at UCSB.

• Xiao Yi, Terence Tao, and James Maynard confirmed that their project payments had arrived, and Kleinrock thanked Xiao Yi for helping speed up the transfer.
• Terence Tao and Maynard said goodbye to Xiao Yi, who left with Zhang Yitang for Santa Barbara.
• On the drive, Xiao Yi mistook a passing mounted police officer for a reminder of the game Road Rash, then reviewed Zhang Yitang’s research notes on the Landau-Siegel Zero Conjecture.
• After reaching UCSB and settling into the student dormitories, Xiao Yi and Zhang Yitang went to Zhang Yitang’s office to discuss the conjecture’s remaining problems.

Xiao Yi combined the circle method with Xiao's expansion to break through the central obstacle in the Siegel-Zero Conjecture. After he and Zhang Yitang resolved the remaining minor issues over the following days, they completed the proof and established that no Landau-Siegel zero existed.

• Xiao Yi shifted from their earlier approach and began applying the circle method to the problem.
• Xiao Yi combined the circle method with Xiao's expansion, revealing a way past the main obstacle in the proof.
• Zhang Yitang realized the breakthrough had brought them close to a complete proof and decided to continue working with Xiao Yi.
• Xiao Yi returned to his dormitory and studied how the circle method and Xiao's expansion might lead to further techniques, including for the Goldbach Conjecture.
• Over the next several days, Xiao Yi and Zhang Yitang resolved the remaining issues and completed the proof of the Siegel-Zero Conjecture.

After Xiao Yi and Zhang Yitang concluded that Landau-Siegel zeros do not exist, they reflected on the discovery and began preparing a paper. While Zhang Yitang organized their proof, Xiao Yi continued studying the circle method and Xiao's expansion and found a possible connection to prime factorization.

• Zhang Yitang and Xiao Yi finished their proof and concluded that the Landau-Siegel zero does not exist.
• Xiao Yi and Zhang Yitang discussed how unexpected discoveries could lead to major advances in mathematics and physics.
• Zhang Yitang explained that he would organize the paper, and Xiao Yi offered to help if problems arose.
• Over the following days, Zhang Yitang worked on the paper while Xiao Yi studied the circle method and Xiao's expansion.
• Xiao Yi unexpectedly realized that the method might help with prime factorization.

Xiao Yi turned his new prime-factorization method into the basis for Bitcoin mining software and planned how to charge miners for using it. After Zhang Yitang submitted their joint paper on the Siegel-Zero Conjecture, he offered to introduce Xiao Yi to a mining-farm owner who could help promote the software.

• Xiao Yi combined the circle method with Xiao's expansion to devise an efficient method for factoring prime numbers.
• Xiao Yi began developing mining software with usage fees and a one-percent mining commission, while considering how to protect and promote it.
• Zhang Yitang handed Xiao Yi his paper, and Xiao Yi found typos and citation errors that they corrected together.
• Zhang Yitang uploaded their joint paper to arXiv and invited Xiao Yi to give talks, but Xiao Yi declined.
• Xiao Yi told Zhang Yitang he was writing Bitcoin mining software, and Zhang Yitang offered to introduce him to a mining-farm owner with more than thirty thousand rigs.

Xiao Yi arranged for mining-company owner Huang Houping to test his upcoming mining software, while Zhang Yitang announced that their proof of the Landau-Siegel Zero Conjecture was on arXiv. The paper passed review and was released, leaving mathematicians eager to examine its proof.

• Zhang Yitang introduced Xiao Yi to Huang Houping, who agreed to test Xiao Yi’s mining software free for three days once it was finished.
• Xiao Yi learned Huang Houping’s mining company could help spread the software if it improved mining profits.
• Zhang Yitang announced that his and Xiao Yi’s paper, “The Nonexistence of Landau-Siegel Zeros,” had been uploaded to arXiv.
• Joey Ayton visited Zhang Yitang and learned that Xiao Yi had helped solve the Zero Conjecture in less than a day.
• Mathematicians gathered on arXiv, and the paper passed review and was publicly released.

Terence Tao and James Maynard reacted to Zhang Yitang and Xiao Yi’s proof of the Landau-Siegel Zero Conjecture, praising its new methods but complaining about its abbreviated proofs. After the pair returned to China, Zhang Yitang found that mathematicians had flooded him with comments telling him to stop writing papers, and he prepared to argue back.

• Terence Tao read Zhang Yitang and Xiao Yi’s proof of the Landau-Siegel Zero Conjecture and recognized Xiao Yi’s contribution to Xiao’s Circle Method Expansion.
• James Maynard called Terence Tao, and they discussed the proof’s speed and Zhang Yitang’s difficult writing style.
• The proof spread through the mathematical community, where scholars admired its methods but criticized its abbreviated proofs.
• Zhang Yitang and Xiao Yi landed at Shangjing International Airport, and Zhang Yitang found numerous comments telling him to leave paper-writing to Xiao Yi.
• Zhang Yitang vowed to scold his critics, and he and Xiao Yi left the plane and stepped out into familiar surroundings in China.

After returning to China, Xiao Yi reunited with his parents for Lunar New Year and used his earnings to plan a new home for them. Once the holiday ended, he returned to school to set up his mining software server and apply for university startup support.

• Xiao Yi declined to present at the Mathematics Research Institute and flew back to Fei City on Lunar New Year's Eve.
• Xiao Yi reunited with Father Xiao and Mother Xiao, shared his recent experiences, and persuaded them to buy a home in Emerald Court with his earnings.
• Xiao Yi transferred twenty million yuan to his parents for the house and renovations after they visited relatives during the holiday.
• Xiao Yi returned to campus on the eighth day of the Lunar New Year and told Liu Bin he wanted to get his server running.
• Liu Bin gave Xiao Yi an entrepreneurship application form, and Xiao Yi applied for funding for Blockchain Technology Innovation Practice under the company name Yishui Technology.

Xiao Yi got his blockchain mining software approved for a university entrepreneurship space, then configured its server and launched a test with Boss Huang’s mining rigs. His overnight solo test unexpectedly earned 6.25 Bitcoins, leaving him eager to prove Yishui Bit’s algorithm at scale.

• Cao Nan approved Xiao Yi’s blockchain software project and showed him the university space for his server.
• Xu Ming and Junior Brother Hu discovered that the server they had hoped to borrow belonged to Xiao Yi.
• Xiao Yi configured the server and contacted Boss Huang to prepare his mining rigs for Yishui Bit.
• Boss Huang logged in with 3,000 mining rigs, and Xiao Yi confirmed the software was running normally.
• Xiao Yi saw that his overnight test had earned 6.25 Bitcoins, worth about 2.23 million yuan.

Huang Houping tested Xiao Yi’s Yishui Bit mining software and discovered that it raised his mining rigs’ earnings by about 86%. He switched his farm to the software, invested in cloud mining, and offered to pay and promote it, while Xiao Yi refused to sell the algorithm.

• Huang Houping ordered 3,000 mining rigs to join a mining pool through Yishui Bit and test its new algorithm.
• After the first block was mined, Huang Houping and his employees saw average earnings rise from 0.00031229 to 0.00058212 Bitcoin per rig and were stunned.
• Huang Houping monitored the results for about an hour, confirmed earnings stayed near 0.00058 Bitcoin, and ordered the farm to switch its rigs to Yishui Bit and rent cloud servers.
• Huang Houping offered to pay for the software and promote it to mining farms, but Xiao Yi said he would not sell the software or algorithm.
• Xiao Yi agreed to make Yishui Bit available for download in a few days, and Huang Houping offered to help spread the word among miners.

Xiao Yi agreed to let Luo Mingya's materials science research group rent his server and join their computational materials project. He also realized his server was nearing capacity as Huang Houping prepared to promote Xiao Yi's mining software.

• Xiao Yi accepted Huang Houping's offer to promote his software after granting the promised three free days.
• Luo Mingya and four graduate students from the School of Materials Science asked to rent Xiao Yi's server for their research simulations.
• Luo Mingya invited Xiao Yi to join her Computational Materials Science research group, and he agreed.
• Luo Mingya assigned Xu Ming responsibility for data processing, while Xiao Yi's server usage reached 78 percent.
• Xiao Yi explained his mining software project to the students, who were surprised that a major mining boss was already using it.

Xiao Yi visited Luo Mingya’s materials science laboratory and learned about its equipment and unusual advisor-student dynamic. Luo Mingya gave him tensile-test data from metal alloy samples, and he began analyzing it by proposing a Fourier Transform.

• Xiao Yi agreed to expand his server setup and help Xu Ming with data analysis, while Luo Mingya assigned Xu Ming lab cleanup duties for a month.
• Luo Mingya invited Xiao Yi to visit the School of Materials Science laboratory, where he saw her impressive academic poster and toured the lab with Zhao Yuanyuan.
• Xiao Yi watched Luo Mingya confront her advisor, Sun Lina, for playing a Switch instead of working.
• Luo Mingya gave Xiao Yi stress-strain data from alloy tensile tests and asked him to investigate why some samples were weaker.
• Xiao Yi said they should use a Fourier Transform to process the data.

Xiao Yi used Fourier analysis to identify unusual oscillations in Zhao Yuanyuan’s metal samples and linked them to lattice defects, helping Luo Mingya confirm the cause. The findings advanced the project, and Luo Mingya invited Xiao Yi to join research on defects in two-dimensional materials.

• Xiao Yi suggested converting the samples’ stress-strain data into frequency-domain spectra, and Luo Mingya led the students to analyze it on a computer.
• Xiao Yi and Luo Mingya found that abnormal samples had distinct oscillation peaks, and Xiao Yi connected them to possible lattice defects or dislocations.
• Luo Mingya inferred that lattice defects were responsible and directed Zhao Yuanyuan and the other students to conduct further experiments.
• Xiao Yi explained his reasoning to Xu Ming and Liu Chao, then quickly proved that pi cubed was greater than 31 using an estimate and a written calculation.
• Zhao Yuanyuan reported that the team had confirmed a lattice-defect problem and offered to buy Xiao Yi milk tea.
• Luo Mingya invited Xiao Yi to officially join the project studying defects in two-dimensional materials using Density Functional Theory and first-principles calculations.

Luo Mingya explained the lab’s WS2 nanomaterials project to Xiao Yi and asked him to review its computational algorithm. Xiao Yi proposed optimizations and began modifying the code, while Luo Mingya explained that the calculations required more computing power than the school’s old server could provide.

• Luo Mingya introduced TMD materials and described the project’s goal of calculating the optoelectronic properties of 2H/3R polytypes in WS2 nanomaterials.
• Sun Lina stopped playing Breath of the Wild after Luo Mingya threatened to complain about her, and the two joked about the lab’s funding and an expensive server.
• Xiao Yi asked about first-principles calculations and learned that the project involved quantum physics and computational materials science.
• Xu Ming showed Xiao Yi the lab’s theoretical model and algorithm, and Xiao Yi recommended a more efficient iterative solver, multigrid methods, and adaptive mesh refinement.
• Xiao Yi backed up the existing code and began modifying the algorithm for a small-scale test, while Luo Mingya explained that the calculations demanded more computing power than the school’s antique server could provide.

Xiao Yi optimized the lab’s algorithm and began studying computational materials science, while Luo Mingya’s team continued its research. He also watched his new server cluster being installed and received payment from Boss Huang, who reported strong interest in Yishui Bit.

• Xiao Yi optimized the lab’s algorithm, and a small-scale simulation showed over twenty percent better resource utilization along with improved convergence speed and accuracy.
• Luo Mingya teased Sun Lina with a recording, then the team returned to work on their projects while Xiao Yi began studying Density Functional Theory and related topics.
• Xiao Yi spent several days studying computational materials science and considered whether mathematical optimization could improve exchange-correlation functionals.
• Workers began assembling the five-million-yuan server cluster Xiao Yi had purchased at the startup center.
• Boss Huang told Xiao Yi he had transferred 1.5 million yuan in Yishui Bit usage fees and said he had promoted the software, with at least two hundred thousand mining rigs potentially set to use it.

Xiao Yi expanded his server capacity and arranged a possible data-center partnership as Yishui Bit prepared to launch. He then helped Luo Mingya improve her research calculations, leaving Xu Ming and Liu Chao amazed by his expertise.

• After Boss Huang predicted at least two hundred thousand Yishui Bit users, Xiao Yi ordered another three million yuan in servers from Manager Yu.
• Manager Yu suggested server hosting and financing, and Luo Mingya offered to connect Xiao Yi with her brother Luo Mingchuan, who ran a data center.
• Luo Mingya tested her research algorithm on the newly assembled server cluster, but the calculated energy-loss spectrum differed from experimental results.
• Xiao Yi suggested doubling the number of bands to account for bulk plasmon peaks, and the revised calculation produced results closer to the experimental values.
• Xiao Yi proposed doping, molecular dynamics, and mechanical-property simulations, leaving Xu Ming and Liu Chao stunned by how much he knew.

Xiao Yi agreed to carry out three simulations for Luo Mingya’s research project and partnered with Luo Mingchuan to operate Yishui Bit. After the New Year’s Day holiday, the software launched from Luo Mingchuan’s data center and attracted more than three hundred thousand mining machines.

• Xiao Yi offered to handle the doping, molecular dynamics, and mechanical simulations, and Luo Mingya promised him co-first authorship if he completed them.
• Luo Mingya introduced Xiao Yi to her brother Luo Mingchuan, who ran a data center, and Xiao Yi proposed that he provide servers and personnel in exchange for a 40 percent stake in Yishui Bit.
• Luo Mingchuan accepted the deal and agreed to prepare the contract, which he signed with Xiao Yi the next day.
• Xiao Yi delayed Yishui Bit’s launch again, then promised Boss Huang it would launch after the New Year’s Day holiday.
• Yishui Bit moved into Luo Mingchuan’s data center, and more than three hundred thousand mining machines connected to its servers on January 16, which the chapter also called February 27.

After returning to his dorm, Xiao Yi heard that Yishui Bit had passed 500,000 users, while the sudden influx of mining rigs overwhelmed Luo Mingchuan’s servers and drew global attention to the platform. Xiao Yi left the business to Luo Mingchuan and spent the next half month researching Computational Materials Science.

• Xiao Yi reunited with Ye Cheng and the other roommates, told them about his recent work, and agreed to treat them to dinner.
• Luo Mingchuan told Xiao Yi that Yishui Bit had surpassed 500,000 users and was dominating crypto discussions.
• A surge of mining rigs, including Bitmain’s, filled Yishui Bit’s servers, so Luo Mingchuan activated backup capacity and prepared for overseas users.
• Crypto forums spread news of Yishui Bit’s algorithm, Bitmain’s plans to adopt it, and a miner who had earned 6.25 Bitcoin with three rigs.
• Yishui Bit’s popularity spread overseas, while Xiao Yi left its management to Luo Mingchuan and focused on Computational Materials Science for half a month.

Xiao Yi completed three computational models and found that their results closely matched experimental data. As the group prepared further simulations, he proposed a new computational framework combining quantum path integrals with Markov chain Monte Carlo.

• Xiao Yi brought his completed models to Luo Mingya's lab, where the group compared their results with experimental data and found very small errors.
• Luo Mingya praised Xiao Yi's work and led the group to the Entrepreneurship Center to run simulations under different conditions.
• Liu Chao presented a joking proof about π cubed being greater than 31, and Xu Ming teased him with a mock score of zero.
• Xiao Yi returned Luo Mingya's books and said existing material-prediction methods struggled to balance accuracy and computational cost.
• Xiao Yi asked Luo Mingya whether path integrals and Markov chain Monte Carlo could be combined into a new computational framework, leaving her astonished.

Xiao Yi explained his Absolute Electronic Computation idea to Luo Mingya, who offered Materials Science data and assistance. After Luo Mingya left to continue her group’s project, Xiao Yi returned to developing the new method, considering how to combine path integrals with multiscale modeling.

• Xiao Yi described using path integrals, Markov chain Monte Carlo, and machine learning to predict material properties, and Luo Mingya said the approach was credible but difficult to implement.
• Luo Mingya offered to help Xiao Yi with Materials Science questions and provide data, while Zhao Yuanyuan struggled to follow their technical discussion.
• Xu Ming announced that the results showed comparable band structures and similar bulk plasmon peak energies among the studied polytypes.
• Luo Mingya took her fellow students back to the lab to find TMD-based heterostructures and told Xiao Yi to focus on his research, promising he would not be excluded from first authorship.
• Xiao Yi reviewed his derivations for Absolute Electronic Computation and considered combining path integrals, Molecular Dynamics, and finite element analysis into a multiscale framework.

Xiao Yi completed the theoretical model for Absolute Electronic Computation and joked with his roommates after they mistook a project meeting with Luo Mingya for a date. Zhang Yitang then called him during a Princeton presentation, where Xiao Yi answered Manjul Bhargava’s question about controlling higher-order terms in the Circle Method Expansion.

• Xiao Yi finished the theoretical model for Absolute Electronic Computation and planned to begin implementing it on a computer.
• Ye Cheng, Song Ziyang, and Luo Qiao confronted Xiao Yi with a photo of him dining with Luo Mingya, but Xiao Yi explained they had met to discuss their project.
• Xiao Yi bribed Song Ziyang and Luo Qiao with dinner, and they helped him subdue Ye Cheng before he tickled him.
• Zhang Yitang called Xiao Yi from Princeton University after Manjul Bhargava asked how their Circle Method Expansion controlled errors from higher-order terms.
• Xiao Yi explained an adaptive weighting method combined with a sieve method, and Manjul Bhargava accepted the answer.

Xiao Yi demonstrated how his method could control high-order terms in Fourier expansion, then finished training version 1.0 of his Absolute Electronic Computation model. Initial tests on silicon and copper produced results with less than one percent error, leaving him impressed by the model’s accuracy and speed.

• Xiao Yi explained how his method could reduce accumulated errors in Fourier expansion, with Zhang Yitang writing the steps on the blackboard.
• Xiao Yi answered no further questions, then told Zhang Yitang and the assembled scholars that he was working on an important project with practical applications.
• After the livestream ended, Xiao Yi joked with Ye Cheng, Song Ziyang, and Luo Qiao about speaking before hundreds of people.
• The next day, Xiao Yi completed version 1.0 of Absolute Electronic Computation and ran it on his server using experimental data from Luo Mingya.
• A week later, Xiao Yi found training complete and tested silicon and copper; the model’s calculated values differed from measured results by less than one percent.

Xiao Yi tested Absolute Electronic Computation on complex materials and found it produced highly accurate predictions. After Luo Mingya used the model to uncover new questions in her WS2 project, she canceled the celebration and returned to the laboratory with her students.

• Xiao Yi began calculations on methylammonium lead iodide and Yttrium Barium Copper Oxide to test his model on complex materials.
• Luo Mingya and Xu Ming told Xiao Yi their project was finished and an editor at Nature had invited them to submit their paper.
• Xiao Yi reviewed the new calculations, which closely matched experimental results for both materials, and Luo Mingya asked him to test WS2.
• Luo Mingya saw discrepancies in the WS2 results that suggested further research and canceled the celebration dinner so her students could resume experiments.
• Luo Mingya praised Absolute Electronic Computation as a revolutionary achievement and left with her students to continue their work.

Xiao Yi submitted his new Absolute Electronic Computation paper to arXiv while continuing to work on the Goldbach Conjecture. After Manjul Bhargava and Ali Yazdani read the paper’s startling results, Yazdani left to verify them in the lab.

• Xiao Yi posted his Absolute Electronic Computation paper in arXiv’s physics section.
• Bhargava told Yazdani that Xiao Yi had recently pursued applied mathematics and might produce useful results.
• Students nearby noticed Xiao Yi’s new paper, prompting Bhargava and Yazdani to look it up.
• Bhargava and Yazdani read that the model predicted properties of complex materials, including YBCO, with errors under ten percent.
• Yazdani was shocked by the results and said he would return to the lab to verify them.

Researchers in Materials Science and Condensed Matter Physics tested Xiao Yi’s Absolute Electronic Computation model and reported highly accurate predictions for complex materials. At UC Berkeley, Paul Alivisatos told his students that the model could transform research as a valuable experimental tool and defended Xiao Yi’s mathematical expertise.

• Yazdani hurried away to verify the potential of Xiao Yi’s work while Balgava watched him go.
• Researchers in Materials Science and Condensed Matter Physics devoted time and resources to testing Absolute Electronic Computation, with some launching dedicated projects.
• Laboratories at ETH Zurich, Princeton, and elsewhere reported that the model’s predictions for superconductors, topological insulators, and other complex materials closely matched experimental results.
• UC Berkeley students debated the model’s likely impact, and Paul Alivisatos said it could change laboratory habits by assisting experiments without replacing them.
• Paul Alivisatos explained that Xiao Yi’s mathematical methods enabled the breakthrough and suggested that his students improve their mathematics, leaving them horrified.

A week after Xiao Yi published his paper on Absolute Electronic Computation, physicists debated whether the method could be extended to particle research, while scientists weighed its promise against the risks of relying too heavily on computation. Xiao Yi stayed out of the debate and finally attended Luo Mingya's research group's celebration banquet.

• Particle physicists discussed using Xiao Yi's method to simulate collider experiments and asked Edward Witten to assess whether it could be extended to other particles.
• Edward Witten said the mathematical problems were difficult, praised Xiao Yi's ability to unite disparate methods, and suggested asking Xiao Yi to study Theoretical Physics.
• Domestic researchers discussed Absolute Electronic Computation, with some laboratories preparing to adopt it widely and critics warning that it could cause scientists to overlook unknown mechanisms and undervalue experiments.
• Xiao Yi declined to weigh in on how the scientific community should use his method and trusted researchers to make their own decisions.
• Xiao Yi attended Luo Mingya's research group's celebration banquet.